[remotemass (OP)]

What be the pressure (at the sea level) in a column of water of diameter 1 meter in atm (atmosphere units)?

Assume the external walls can hold any pressures.

- remotemass

[Kryptid]

What is the height of the column?

[Petrochemicals]

What is the height of the column?

Homework question

[remotemass (OP)]

Please assume I am targeting escaping gravity and having negligible friction with atmosphere.
So, let's say, 10 million meters.

- remotemass

[alancalverd]

The the pressure at the bottom will be ten million tonnes per square meter or thereabouts.

[evan_au]

I am targeting escaping gravity

How does a big column of water help you do that?

[alancalverd]

Climb in, inflate your lifejacket, and fly out at the top. If you wear two lifejackets you will have a constant 150N upward force acting over 10⁷ meters. Not sure if that equals escape speed but that's an exercise for the reader.

[Bored chemist]

Climb in, inflate your lifejacket, and fly out at the top. If you wear two lifejackets you will have a constant 150N upward force acting over 10⁷ meters. Not sure if that equals escape speed but that's an exercise for the reader.

I think you would reach terminal velocity.
You would need to inflate the lifejacket with something other than a gas.
I gather gasoline is the usual choice.
Not sure how well it would work.

[Petrochemicals]

The diameter has no bearing on the pressure in the water, the column hydrostatic head is the same pressure regardless of diameter. Pressure is equal in all directions.

[alancalverd]

You would need to inflate the lifejacket with something other than a gas.
I gather gasoline is the usual choice.

Funny, that. All mine say carbon dioxide. Who do you fly with?

[Bored chemist]

Funny, that. All mine say carbon dioxide.

The the pressure at the bottom will be ten million tonnes per square meter or thereabouts.

What's the density of CO2 under the sort of pressure you get at that depth?

Anyway...
"Piccard's second bathyscaphe was actually a third vessel Trieste, which was purchased by the United States Navy from Italy in 1957.[1] It had two water ballast tanks and eleven buoyancy tanks holding 120,000 litres (26,000 imp gal; 32,000 US gal) of gasoline.[2]"
from
https://en.wikipedia.org/wiki/Bathyscaphe

[alancalverd]

You are correct - pretty well anything will liquefy under 10⁷ m water gauge. Gasoline will only give you 25% of the lift of gaseous CO2 for a given volume so you might need more than one lifejacket, and some ballast weights to get you to the bottom of the tank in the first place.

Nevertheless it is an intriguing thought. Terminal speed will depend on the available lift force but since the speed of sound in water is more than 4 times that in air, you won't encounter shockwave problems below 3000 mph. That's still some way to go before escape or orbital speed, but still interesting.

I can see a Jules Verne/James Bond  story in the making. Captain Nemo launches a hypersonic glide bomb made from a Lada petrol tank, from the bottom of the Marianas Trench. "The problem, 007, is that the aircraft leaves the surface vertically at 3000 mph with no apparent power source. Spectral analysis shows that it is filled with Tesco's Premium but doesn't emit any CO2." "Very green, Moneypenny. But the baddies always use Porsche 911s." 

[Bored chemist]

You are correct - pretty well anything will liquefy under 10^7 m water gauge.

I suspect that quite a few things would solidify including water. Unless your prospective astronaut is happy to be "boiled", you have a problem.
If I'm reading this correctly, the melting point of water at that depth would be well over 300C
https://en.wikipedia.org/wiki/Phase_diagram#Crystals

[Bored chemist]

some ballast weights to get you to the bottom of the tank in the first place.

By the time you have hauled them to the top of the tank...
This is essentially a very inefficient way of making a ballista.

Having said that, it's probably still better than trying to store energy as antimatter.

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